Windowing methods (Hamming, Hanning, Blackman) in Signal Processing - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Hamming window array

What is the output array when applying a Hamming window of length 5 using numpy?

Signal Processing

import numpy as np
np.set_printoptions(precision=4, suppress=True)
window = np.hamming(5)
print(window)

A [0.42 0.5 1. 0.5 0.42 ]

B [0.08 0.3979 0.9129 0.9129 0.3979]

C [0.08 0.54 1. 0.54 0.08 ]

D [0.0 0.5 1. 0.5 0.0 ]

💡 Hint

Recall that the Hamming window starts and ends near 0.08, not zero.

The Hamming window of length 5 produces values starting and ending near 0.08, with middle values higher. Option C matches the numpy output.

❓ data_output

intermediate

Length of Blackman window output

What is the length of the array returned by numpy.blackman when called with argument 7?

Signal Processing

import numpy as np
window = np.blackman(7)
print(len(window))

A 5

B 6

C 8

D 7

💡 Hint

The window length parameter defines the output array length exactly.

The numpy.blackman function returns an array of the exact length specified by the input argument.

🧠 Conceptual

advanced

Main difference between Hanning and Hamming windows

Which statement best describes the main difference between Hanning and Hamming windows?

A Hanning window has zero values at the edges, Hamming window has non-zero edges.

B Hamming window has zero values at the edges, Hanning window has non-zero edges.

C Both windows have zero values at the edges but differ in peak amplitude.

D Both windows have non-zero edges but differ in length.

💡 Hint

Think about the values at the start and end of each window.

The Hanning window starts and ends at zero, while the Hamming window starts and ends near 0.08, not zero.

❓ visualization

advanced

Plot comparison of Hamming, Hanning, and Blackman windows

Which option produces a plot showing all three windows of length 50 on the same graph with clear labels?

Signal Processing

import numpy as np
import matplotlib.pyplot as plt
N = 50
hamming = np.hamming(N)
hanning = np.hanning(N)
blackman = np.blackman(N)
plt.plot(hamming, label='Hamming')
plt.plot(hanning, label='Hanning')
plt.plot(blackman, label='Blackman')
plt.legend()
plt.title('Window Functions Comparison')
plt.show()

A Plots Blackman window only with incorrect title.

B Plots all three windows with labels and title correctly.

C Plots only Hamming and Hanning windows without labels.

D Plots all three windows but missing legend and title.

💡 Hint

Look for code that includes all three plots, labels, legend, and title.

Option B includes plotting all three windows with labels, legend, and title, making the visualization clear and complete.

🔧 Debug

expert

Identify error in window function usage

What error will this code raise? import numpy as np w = np.hamming(-10) print(w)

Signal Processing

import numpy as np
w = np.hamming(-10)
print(w)

A ValueError: window length must be non-negative

B SyntaxError: invalid syntax

C TypeError: unsupported operand type(s) for -: 'int' and 'str'

D No error, prints an empty array

💡 Hint

Window length cannot be negative.

Numpy raises a ValueError if the window length is negative.

Practice

1. What is the main purpose of applying a windowing method like Hamming or Hanning to a signal before frequency analysis?

easy

A. To reduce spectral leakage by smoothing signal edges

B. To increase the signal amplitude uniformly

C. To convert the signal from time domain to frequency domain

D. To remove noise from the signal completely

Solution

1. Step 1: Understand windowing effect on signal edges

   Windowing methods multiply the signal by a smooth curve to reduce abrupt edges.

2. Step 2: Connect windowing to spectral leakage reduction

   Smoothing edges reduces spectral leakage, which improves frequency analysis accuracy.

3. Final Answer:

   To reduce spectral leakage by smoothing signal edges -> Option A

4. Quick Check:

   Windowing reduces leakage [OK]

Hint: Windowing smooths edges to reduce leakage [OK]

Common Mistakes:

• Thinking windowing increases amplitude
• Confusing windowing with Fourier transform
• Assuming windowing removes all noise

2. Which of the following is the correct Python syntax to generate a Hamming window of length 64 using NumPy?

easy

A. np.hamming(64)

B. np.hanning(64)

C. np.blackman(64)

D. np.window('hamming', 64)

Solution

1. Step 1: Recall NumPy window function names

   NumPy provides np.hamming(), np.hanning(), and np.blackman() functions for windows.

2. Step 2: Identify correct function for Hamming window

   np.hamming(64) generates a Hamming window of length 64 correctly.

3. Final Answer:

   np.hamming(64) -> Option A

4. Quick Check:

   Hamming window function = np.hamming() [OK]

Hint: Use np.hamming(length) for Hamming window [OK]

Common Mistakes:

• Using np.hanning() for Hamming window
• Trying np.window() which doesn't exist
• Confusing window length parameter

3. What will be the output shape of the following code snippet?

import numpy as np
window = np.blackman(100)
print(window.shape)

medium

A. (100, 1)

B. (1, 100)

C. (100,)

D. 100

Solution

1. Step 1: Understand np.blackman output type

   np.blackman(n) returns a 1D NumPy array of length n.

2. Step 2: Check shape of 1D array

   A 1D array of length 100 has shape (100,), not a 2D shape or integer.

3. Final Answer:

   (100,) -> Option C

4. Quick Check:

   1D array length 100 shape = (100,) [OK]

Hint: Window functions return 1D arrays with shape (length,) [OK]

Common Mistakes:

• Expecting 2D shape like (1, 100)
• Confusing shape with length integer
• Assuming output is a matrix

4. Identify the error in this code snippet that tries to apply a Hanning window to a signal array:

import numpy as np
signal = np.array([1, 2, 3, 4, 5])
window = np.hanning(10)
windowed_signal = signal * window
print(windowed_signal)

medium

A. Signal array must be 2D for windowing

B. np.hanning() is not a valid function

C. Multiplication operator * cannot be used here

D. Window length does not match signal length

Solution

1. Step 1: Check lengths of signal and window

   Signal length is 5, but window length is 10, so sizes mismatch.

2. Step 2: Understand element-wise multiplication requirement

   Element-wise multiplication requires arrays of the same length.

3. Final Answer:

   Window length does not match signal length -> Option D

4. Quick Check:

   Lengths must match for multiplication [OK]

Hint: Signal and window must have same length [OK]

Common Mistakes:

• Assuming np.hanning() is invalid
• Thinking * operator can't multiply arrays
• Believing signal must be 2D

5. You have a noisy signal of length 256. You want to minimize spectral leakage while keeping the main lobe width narrow for better frequency resolution. Which window should you choose?

hard

A. Hanning window

B. Hamming window

C. Blackman window

D. Rectangular window

Solution

1. Step 1: Understand window trade-offs

   Blackman reduces leakage most but has wider main lobe (lower resolution).

2. Step 2: Compare Hamming and Hanning

   Hamming has better leakage reduction than Hanning and narrower main lobe than Blackman.

3. Step 3: Choose window balancing leakage and resolution

   Hamming is best for minimizing leakage while keeping main lobe narrow.

4. Final Answer:

   Hamming window -> Option B

5. Quick Check:

   Best leakage and resolution balance = Hamming [OK]

Hint: Hamming balances leakage reduction and resolution best [OK]

Common Mistakes:

• Picking Blackman for narrow main lobe
• Choosing rectangular window ignoring leakage
• Confusing Hanning and Hamming properties